Answer:
Step-by-step explanation:
-2x=10-3(2x+6) next step is to distribute -3 in the parenthesis,
-2x=10-6x-18
ABCSolve for x
x + 30 + 2x - 4 + 4x = 180 All triangles have 180°. collect like terms.
7x + 26 = 180 subtract 26 to both sides.
7x = 154 Divide by 7
x = 154/7
x = 22
A = x + 30 = 22 + 30 = 52
B = 2x - 4 = 2(22) + 30 = 44 - 4 = 40
C = 4x = 4*22 = 88
Check<A + <B + <C = 180
<52 + <40 + <88 = 180°
180 = 180
It checks and we are done with this triangle.
A'B'C'
2x + 8 + x + 18 + 5x - 22 = 180 Collect the like terms.
8x + 4 = 180 Subtract 4 from both sides.
8x = 180 - 4
8x = 176 Divide by 8
x = 176 / 8
x = 22
A' = 2x + 8
A' = 2(22) + 8 = 44 + 8 = 52
B' = x + 18 = 22 + 18 = 40
C' = 5x - 22 = 5*22 - 22 = 110 - 22 = 88
ConclusionA = A'
B = B'
C = C'
All three angles of one triangle are equal to all three angles of the other. So by AA the two triangles are similar.
CommentNote: the dilation of 12 has nothing to do with this answer. If you were asked about similarity of sides then the 12 would be something to do with the problem.
3 feet by 5 feet is the original figure.
We can obviously say that the triangle falls into the Not Similar - Different Shape category since it is a triangle, and we were given a rectangle
We can obviously say that the parallelogram (right next to the triangle) falls into the Not Similar - Different Shape category since it is a parallelogram, and we were given a rectangle
The 3 feet by 4 feet falls into the category of Not similar - Different ratio of Side Lengths because the original was 3 feet by 4 feet. And so then one side remained the same while the other went decreased, so they are not in a ratio.
The 12 feet by 15 feet falls into the category of Not similar - Different ratio of Side Lengths because 12 feet by 15 feet can be simplified in a ratio of 4 to 5 while the original is 3 to 5
The 6 feet by 10 feet falls into the category of Similar because 6 feet by 10 feet can be simplified in a ratio of 3 to 5 and the original is 3 to 5.
The 3 feet by 5 feet falls into the category of Similar because it is the same exact figure just rotated!
Answer:
both 45 degrees
Step-by-step explanation:
90 + 45 + 45 = 180 degrees
Hope this helps!
I would invest $500 to be compounded as Compound Interest is $1,540,250 while Simple Interest is $50.
<u>Step-by-step explanation:</u>
Step 1:
Calculate simple interest in the first case. Given details are Principal (P) = $500, Rate (R) = 5% and Time (T) = 2 years
⇒ Simple Interest (SI) = PRT/100 = 500 × 5 × 2/100 = $50
Step 2:
Calculate compounded interest for the second case. Given details are Principal (P) = $500, Interest rate (r) = 3%, Number of times it is compounded (n) = 12, time (t) = 2 years
⇒ Compound Interest (CI) = [P (1 + r/n)^n × t] - P
⇒ CI = [500 (1 + 3/12)^12 × 3] - 500
⇒ CI = [500 (1 + 1/4)^36] - 500
⇒ CI = [500 (5/4)^36] - 500
⇒ CI = [500 × 3081.5] - 500 = 1540750 - 500
⇒ CI = $1,540,250
